# Communities as Well Separated Subgraphs with Cohesive Cores: Identification of Core-Periphery Structures in Link Communities

Conference paper

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## Abstract

Communities in networks are commonly considered as highly cohesive subgraphs which are well separated from the rest of the network. However, cohesion and separation often cannot be maximized at the same time, which is why a compromise is sought by some methods. When a compromise is not suitable for the problem to be solved it might be advantageous to separate the two criteria. In this paper, we explore such an approach by defining communities as well separated subgraphs which can have one or more cohesive cores surrounded by peripheries. We apply this idea to link communities and present an algorithm for constructing core-periphery structures in link communities and first test results.

## Keywords

Networks Communities Link clustering Core and periphery## References

- 1.Ahn, Y.Y., Bagrow, J.P., Lehmann, S.: Link communities reveal multi-scale complexity in networks. Nature
**466**, 761–764 (2010)Google Scholar - 2.Amelio, A., Pizzuti, C.: Overlapping community discovery methods: a survey. In: Social Networks: Analysis and Case Studies, p. 105 (2014)Google Scholar
- 3.Bagrow, J.P., Bollt, E.M.: Local method for detecting communities. Phys. Rev. E
**72**(4), 046,108 (2005). https://doi.org/10.1103/PhysRevE.72.046108Google Scholar - 4.Ball, B., Karrer, B., Newman, M.E.J.: Efficient and principled method for detecting communities in networks. Phys. Rev. E
**84**(3), 036,103 (2011). https://doi.org/10.1103/PhysRevE.84.036103Google Scholar - 5.Borgatti, S.P., Everett, M.G.: Models of core/periphery structures. Soc. Netw.
**21**(4), 375–395 (2000)Google Scholar - 6.Csermely, P., London, A., Wu, L.Y., Uzzi, B.: Structure and dynamics of core/periphery networks. J. Complex Netw.
**1**(2), 93–123 (2013). https://doi.org/10.1093/comnet/cnt016Google Scholar - 7.Evans, T.S., Lambiotte, R.: Line graphs, link partitions, and overlapping communities. Phys. Rev. E
**80**(1), 16,105 (2009)Google Scholar - 8.Fortunato, S.: Community detection in graphs. Phys. Rep.
**486**, 75–174 (2010)Google Scholar - 9.Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. PNAS
**99**, 7821–7826 (2002)Google Scholar - 10.Havemann, F., Gläser, J., Heinz, M.: Memetic search for overlapping topics based on a local evaluation of link communities. Scientometrics 1–30 (2017). https://doi.org/10.1007/s11192-017-2302-5
- 11.Kannan, R., Vempala, S., Vetta, A.: On clusterings: good, bad and spectral. J. ACM
**51**(3), 497–515 (2004). https://doi.org/10.1145/990308.990313Google Scholar - 12.Kojaku, S., Masuda, N.: Finding multiple core-periphery pairs in networks. Phys. Rev. E
**96**(5), 052,313 (2017)Google Scholar - 13.Leskovec, J., Lang, K.J., Mahoney, M.: Empirical comparison of algorithms for network community detection. In: Proceedings of the 19th International Conference on World Wide Web, WWW ’10, pp. 631–640, New York (2010). https://doi.org/10.1145/1772690.1772755
- 14.Liu, D., Su, Y., Li, X., Niu, Z.: A novel community detection method based on cluster density peaks. In: Natural Language Processing and Chinese Computing. Lecture Notes in Computer Science, pp. 515–525. Springer (2017). https://doi.org/10.1007/978-3-319-73618-1_43
- 15.Metzler, S., Günnemann, S., Miettinen, P.: Hyperbolae are no hyperbole: modelling communities that are not cliques. In: Data Mining (ICDM), 2016 IEEE 16th International Conference on Data Mining, pp. 330–339. IEEE (2016)Google Scholar
- 16.Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E
**69**, 026,113 (2004)Google Scholar - 17.Piccardi, C.: Finding and testing network communities by lumped Markov chains. PloS one
**6**(11), e27,028 (2011)Google Scholar - 18.Pizzuti, C.: A multi-objective genetic algorithm for community detection in networks. In: 21st IEEE International Conference on Tools with Artificial Intelligence, pp. 379–386. IEEE (2009)Google Scholar
- 19.Radicchi, F., Castellano, C., Cecconi, F., Loreto, V., Parisi, D.: Defining and identifying communities in networks. PNAS
**101**, 2658–2663 (2004)Google Scholar - 20.Ravasz, E., Barabási, A.L.: Hierarchical organization in complex networks. Phys. Rev. E
**67**(2), 026,112 (2003). https://doi.org/10.1103/PhysRevE.67.026112Google Scholar - 21.Rezvani, M., Wang, Q., Liang, W.: Fast Algorithm for Detecting Cohesive Hierarchies of Communities in Large Networks, pp. 486–494. ACM (2018). https://doi.org/10.1145/3159652.3159704. http://dl.acm.org/citation.cfm?doid=3159652.3159704
- 22.Rossa, F.D., Dercole, F., Piccardi, C.: Profiling core-periphery network structure by random walkers. Sci. Rep.
**3**, 1467 (2013). https://doi.org/10.1038/srep01467Google Scholar - 23.Schaeffer, S.E.: Graph clustering. Comput. Sci. Rev.
**1**(1), 27–64 (2007). https://doi.org/10.1016/j.cosrev.2007.05.001Google Scholar - 24.Shi, J., Malik, J.: Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell.
**22**(8), 888–905 (2000). https://doi.org/10.1109/34.868688Google Scholar - 25.Wang, X., Liu, G., Li, J., Nees, : J.P.: Locating structural centers: a density-based clustering method for community detection. PLOS ONE
**12**(1), e0169,355 (2017). https://doi.org/10.1371/journal.pone.0169355 - 26.Xie, J., Kelley, S., Szymanski, B.K.: Overlapping community detection in networks: the state-of-the-art and comparative study. ACM Comput. Surv.
**45(4), 43:1–43**, 35 (2013). https://doi.org/10.1145/2501654.2501657 - 27.Xu, X., Yuruk, N., Feng, Z., Schweiger, T.A.J.: SCAN: a structural clustering algorithm for networks. In: Proceedings of the 13th ACM SIGKDD, KDD ’07, pp. 824–833. ACM, New York, NY, USA (2007). https://doi.org/10.1145/1281192.1281280
- 28.Yang, J., Leskovec, J.: Defining and evaluating network communities based on ground-truth. Knowl. Inf. Syst.
**42**(1), 181–213 (2013). https://doi.org/10.1007/s10115-013-0693-zGoogle Scholar - 29.Yang, J., Leskovec, J.: Overlapping communities explain core-periphery organization of networks. Proc. IEEE
**102**(12), 1892–1902 (2014)Google Scholar - 30.Zachary, W.: An information flow model for conflict and fission in small groups. J. Anthropol. Res.
**33**(4), 452–473 (1977)Google Scholar - 31.Zhang, X., Martin, T., Newman, M.E.J.: Identification of core-periphery structure in networks. Phys. Rev. E
**91**(3), 032,803 (2015). https://doi.org/10.1103/PhysRevE.91.032803. https://link.aps.org/doi/10.1103/PhysRevE.91.032803

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